Vectors | Chapter 1, Essence of linear algebra

Vectors | Chapter 1, Essence of linear algebra

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Starting the linear algebra sequence with the fundamentals.
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Correction: 6:52, the display ought to present [x1, y1] + [x2, y2] = [x1+x2, y1+y2]

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42 thoughts on “Vectors | Chapter 1, Essence of linear algebra”

  1. Thank you to everyone who pointed out the typo at 6:53, where the component-wise sum should of course be [x1+x2, y1+y2].

    In general, little mistakes in videos like this will be mentioned in the video description.

    Reply

  2. I searched the internet looking for an answer to this question. If a vector V starts at the origin, and vector W has the same magnitude and direction but different initial and terminal points, so they are basically the same vector that are positioned dissimilarly in space. what's the significance of such characteristic (position), and what difference does it make?. every time I search it up, I get hit with "position vectors" which is not really what I'm looking for. I'm an aerospace eng 1st year student, so I guess that I don't need to know. Still, out of curiosity, if you have a reference or an answer I'd appreciate it. 🙂

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  9. i am wondering how you make such presentation , they are wonderfull with all those graphics and animation are you using powerpoint or another tool to make it , and if you are using powerpoint how many time it gets to make one presentation line that ?

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  22. [ @ 0:41 ] Note that the "length" (i.e. "size scale") and "direction" of a "vector" as here described are purely "relative" to — as being defined with respect to and in terms of — the "structure (or 'structural content', if you prefer)" of — the point-radially "surrounding [spatial] environment" that it is employed by the human body's "on-board" 'sensory experiential environment' simulator' faculty (a.k.a. "imagination") to "describe" (map). This 'sensory environment map construction instruction' function that we humans employ our "mathematics" (and 'other' linguistically encoded "specifications") to "describe" is the 'device' (''technology' / "tool") that our species has adaptively ['self-']evolved for primary survival probability enhancing purpose of "sharing" our "on-board" sensory environment maps with our fellow species members without the need to subject their bodies to the same "direct sensory experience" survival risks undergone by the "speaker" in order to obtain those "on-board" maps.

    [Note the "conditional response" behavior "programming" function of both the direct sensory experientially acquired,, and the linguistically instructed "imagination"-(as "sensory-experiential simulator")-produced (as "shared") "on-board" 'sensory environment map'(s)'. Thus the operational functionality (and "utility") of that ubiquitous and age-old linguistic human behavior manipulation 'device' commonly referred to as the "lie", as the conveyance of a deliberately false (and/'or strategically and selectively incomplete) '"external" (i.e. sensory) environment 'map' to a receptive audience by 'trusted source'.]

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  24. Hoy ví a mi hijo universitario, muy muy feliz, porque había entendido este tema gracias a está maravillosa explicación, estoy muy agradecida por la explicación. Me gustaría un día recibirlo en casa, vivo en cuzco Perú. El nombre de mi hijo es Badi y es estudiante de ciencias de la computación.

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  25. I want to congratulate you. The way you explained vector addition as "steps" is absolutely excelent. I've had a Linear Algebra course recently and I was always confused with the visualization of the result of vector addition. But thanks to that beautifully illustrated explanation, it was some sort of "eureka" to my brain. Fantastic job!

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  28. Very good videos! I am a physics engineering student and they were very useful to me!! They are super well explained. Also, if someone is studying linear algebra, I recommend a book called Stanley I. Grossman, which is mathematically more rigorous, and to complement it, I also recommend another one called Howard Anton, Introduction to Linear Algebra. Mathematically, it is not very rigorous, but it does a good job simplifying and explaining. some things. I think it is a good idea to watch all the videos of this linear algebra course and complement what is explained in the video by reading the books!!

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  32. I never learned about matrices or polar coordinates in school and these gaps in my knowledge have always bothered me. Does 3Blue1Brown have any videos that go over the basics of these things? If I'm understanding correctly, when adding vectors, you want them in (x, y) form, but when multiplying them, you want them in (r, theta) form?

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